Multiplying Mixed Numbers Worksheets - 15 Worksheets Library - Free Printable

Let's solve each problem on the worksheet step by step. The task is to multiply mixed numbers and reduce the answers to the simplest form.

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🔧 Steps to Multiply Mixed Numbers:

1. Convert each mixed number to an improper fraction.
2. Multiply the two improper fractions.
3. Simplify the result (reduce to lowest terms).
4. If needed, convert back to a mixed number.

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We'll go through each problem:

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1. $ 3\frac{2}{5} \times 1\frac{4}{10} $

- Convert:
- $ 3\frac{2}{5} = \frac{17}{5} $
- $ 1\frac{4}{10} = \frac{14}{10} = \frac{7}{5} $
- Multiply: $ \frac{17}{5} \times \frac{7}{5} = \frac{119}{25} $
- Convert to mixed number: $ \frac{119}{25} = 4\frac{19}{25} $

✔ Answer: $ 4\frac{19}{25} $

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2. $ 4\frac{3}{6} \times 2\frac{3}{9} $

- Simplify fractions first:
- $ 4\frac{3}{6} = 4\frac{1}{2} = \frac{9}{2} $
- $ 2\frac{3}{9} = 2\frac{1}{3} = \frac{7}{3} $
- Multiply: $ \frac{9}{2} \times \frac{7}{3} = \frac{63}{6} = \frac{21}{2} $
- Convert: $ \frac{21}{2} = 10\frac{1}{2} $

✔ Answer: $ 10\frac{1}{2} $

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3. $ 3\frac{2}{8} \times 2\frac{10}{16} $

- Simplify:
- $ 3\frac{2}{8} = 3\frac{1}{4} = \frac{13}{4} $
- $ 2\frac{10}{16} = 2\frac{5}{8} = \frac{21}{8} $
- Multiply: $ \frac{13}{4} \times \frac{21}{8} = \frac{273}{32} $
- Convert: $ \frac{273}{32} = 8\frac{17}{32} $

✔ Answer: $ 8\frac{17}{32} $

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4. $ 2\frac{12}{20} \times 1\frac{11}{16} $

- Simplify:
- $ 2\frac{12}{20} = 2\frac{3}{5} = \frac{13}{5} $
- $ 1\frac{11}{16} = \frac{27}{16} $
- Multiply: $ \frac{13}{5} \times \frac{27}{16} = \frac{351}{80} $
- Convert: $ \frac{351}{80} = 4\frac{31}{80} $

✔ Answer: $ 4\frac{31}{80} $

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5. $ 4\frac{3}{9} \times 3\frac{2}{8} $

- Simplify:
- $ 4\frac{3}{9} = 4\frac{1}{3} = \frac{13}{3} $
- $ 3\frac{2}{8} = 3\frac{1}{4} = \frac{13}{4} $
- Multiply: $ \frac{13}{3} \times \frac{13}{4} = \frac{169}{12} $
- Convert: $ \frac{169}{12} = 14\frac{1}{12} $

✔ Answer: $ 14\frac{1}{12} $

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6. $ 2\frac{5}{8} \times 1\frac{3}{6} $

- Simplify:
- $ 2\frac{5}{8} = \frac{21}{8} $
- $ 1\frac{3}{6} = 1\frac{1}{2} = \frac{3}{2} $
- Multiply: $ \frac{21}{8} \times \frac{3}{2} = \frac{63}{16} $
- Convert: $ \frac{63}{16} = 3\frac{15}{16} $

✔ Answer: $ 3\frac{15}{16} $

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7. $ 3\frac{2}{4} \times 2\frac{3}{5} $

- Simplify:
- $ 3\frac{2}{4} = 3\frac{1}{2} = \frac{7}{2} $
- $ 2\frac{3}{5} = \frac{13}{5} $
- Multiply: $ \frac{7}{2} \times \frac{13}{5} = \frac{91}{10} $
- Convert: $ \frac{91}{10} = 9\frac{1}{10} $

✔ Answer: $ 9\frac{1}{10} $

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8. $ 5\frac{4}{8} \times 2\frac{6}{9} $

- Simplify:
- $ 5\frac{4}{8} = 5\frac{1}{2} = \frac{11}{2} $
- $ 2\frac{6}{9} = 2\frac{2}{3} = \frac{8}{3} $
- Multiply: $ \frac{11}{2} \times \frac{8}{3} = \frac{88}{6} = \frac{44}{3} $
- Convert: $ \frac{44}{3} = 14\frac{2}{3} $

✔ Answer: $ 14\frac{2}{3} $

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9. $ 4\frac{3}{6} \times 2\frac{5}{9} $

- Simplify:
- $ 4\frac{3}{6} = 4\frac{1}{2} = \frac{9}{2} $
- $ 2\frac{5}{9} = \frac{23}{9} $
- Multiply: $ \frac{9}{2} \times \frac{23}{9} = \frac{207}{18} = \frac{23}{2} $
- Convert: $ \frac{23}{2} = 11\frac{1}{2} $

✔ Answer: $ 11\frac{1}{2} $

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10. $ 3\frac{1}{2} \times 1\frac{1}{4} $

- Convert:
- $ 3\frac{1}{2} = \frac{7}{2} $
- $ 1\frac{1}{4} = \frac{5}{4} $
- Multiply: $ \frac{7}{2} \times \frac{5}{4} = \frac{35}{8} $
- Convert: $ \frac{35}{8} = 4\frac{3}{8} $

✔ Answer: $ 4\frac{3}{8} $

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11. $ 4\frac{1}{7} \times 3\frac{2}{3} $

- Convert:
- $ 4\frac{1}{7} = \frac{29}{7} $
- $ 3\frac{2}{3} = \frac{11}{3} $
- Multiply: $ \frac{29}{7} \times \frac{11}{3} = \frac{319}{21} $
- Convert: $ \frac{319}{21} = 15\frac{4}{21} $

✔ Answer: $ 15\frac{4}{21} $

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12. $ 2\frac{5}{9} \times 1\frac{1}{4} $

- Convert:
- $ 2\frac{5}{9} = \frac{23}{9} $
- $ 1\frac{1}{4} = \frac{5}{4} $
- Multiply: $ \frac{23}{9} \times \frac{5}{4} = \frac{115}{36} $
- Convert: $ \frac{115}{36} = 3\frac{7}{36} $

✔ Answer: $ 3\frac{7}{36} $

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13. $ 3\frac{3}{8} \times 2\frac{2}{5} $

- Convert:
- $ 3\frac{3}{8} = \frac{27}{8} $
- $ 2\frac{2}{5} = \frac{12}{5} $
- Multiply: $ \frac{27}{8} \times \frac{12}{5} = \frac{324}{40} = \frac{81}{10} $
- Convert: $ \frac{81}{10} = 8\frac{1}{10} $

✔ Answer: $ 8\frac{1}{10} $

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14. $ 3\frac{4}{6} \times 1\frac{2}{7} $

- Simplify:
- $ 3\frac{4}{6} = 3\frac{2}{3} = \frac{11}{3} $
- $ 1\frac{2}{7} = \frac{9}{7} $
- Multiply: $ \frac{11}{3} \times \frac{9}{7} = \frac{99}{21} = \frac{33}{7} $
- Convert: $ \frac{33}{7} = 4\frac{5}{7} $

✔ Answer: $ 4\frac{5}{7} $

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15. $ 3\frac{3}{5} \times 2\frac{2}{4} $

- Simplify:
- $ 3\frac{3}{5} = \frac{18}{5} $
- $ 2\frac{2}{4} = 2\frac{1}{2} = \frac{5}{2} $
- Multiply: $ \frac{18}{5} \times \frac{5}{2} = \frac{90}{10} = 9 $

✔ Answer: $ 9 $

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16. $ 2\frac{2}{3} \times 1\frac{4}{7} $

- Convert:
- $ 2\frac{2}{3} = \frac{8}{3} $
- $ 1\frac{4}{7} = \frac{11}{7} $
- Multiply: $ \frac{8}{3} \times \frac{11}{7} = \frac{88}{21} $
- Convert: $ \frac{88}{21} = 4\frac{4}{21} $

✔ Answer: $ 4\frac{4}{21} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 4\frac{19}{25} $ |
| 2 | $ 10\frac{1}{2} $ |
| 3 | $ 8\frac{17}{32} $ |
| 4 | $ 4\frac{31}{80} $ |
| 5 | $ 14\frac{1}{12} $ |
| 6 | $ 3\frac{15}{16} $ |
| 7 | $ 9\frac{1}{10} $ |
| 8 | $ 14\frac{2}{3} $ |
| 9 | $ 11\frac{1}{2} $ |
| 10 | $ 4\frac{3}{8} $ |
| 11 | $ 15\frac{4}{21} $ |
| 12 | $ 3\frac{7}{36} $ |
| 13 | $ 8\frac{1}{10} $ |
| 14 | $ 4\frac{5}{7} $ |
| 15 | $ 9 $ |
| 16 | $ 4\frac{4}{21} $ |

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